Learn Spanish (Latin America): El piso está sucio, lo estoy barriendo.

Yes, you have two choices here! When you use a conjugated verb (like estoy) with a gerund (an -iendo or -ando word like barriendo), the object pronoun lo can go before the conjugated verb (lo estoy barriendo) or attached directly to the end of the gerund (estoy barriéndolo). Both are common and mean the exact same thing.

If I attach lo to the end to make estoy barriéndolo, why does it need an accent mark?

When you attach a pronoun to a gerund, you add an extra syllable to the end of the word. To keep the natural spoken stress on the exact same letter as the original word (barriendo), you must add a written accent mark over the e.

Why do we use está instead of es for the floor being dirty?

We use está (from the verb estar) because being dirty is a temporary condition. You are sweeping it right now, so it will be clean soon! If you used es (from the verb ser), it would sound like the floor is permanently dirty by nature, like a floor made out of dirt.

How do I know whether to use lo or la for "it" in this sentence?